Size of a 2D ring polymer topologically unentangled with a planar array of obstacles

We readdress the statistical mechanical problem of the size of a 2D ring polymer, topologically unentangled with a planar lattice array of regularly spaced obstacles. It is commonly assumed in the literature that such a polymer adopts a randomly branched type of configuration, in order to ostensibly maximise chain entropy, while minimising obstacle entanglement. Via an innovative analytic approach, valid in the condensed polymer region, we are able to provide a greater theoretical understanding, and justification, for this presumed polymer behaviour. Our theoretically derived results could also potentially have important implications for the structure of interphase chromosomes, as well as electrophoretic ring polymer dynamics.